Due to their broadband nonlinear optical properties, low-dimensional materials are widely used for pulse generation in fiber and solid-state lasers. Here we demonstrate novel materials, Bi2Te2Se (BTS) and Sn-doped Bi2Te2Se (BSTS), which can be used as a universal saturable absorbers for distinct spectral regimes. The material was mechanically exfoliated from a bulk single-crystal and deposited onto a side-polished fiber. We have performed characterization of the fabricated devices and employed them in polarization-maintaining ytterbium- and erbium-doped fiber lasers. This enabled us to obtain self-starting passively Q-switched regime at 1 µm and 1.56 µm. The oscillators emitted stable, linearly polarized radiation with the highest single pulse energy approaching 692 nJ. Both lasers are characterized by the best performance observed in all-polarization maintaining Q-switched fiber lasers with recently investigated new saturable absorbers, which was enabled by a very high damage threshold of the devices. This demonstrates the great potential of the investigated materials for the ultrafast photonics community.